Quantum Circuit For Discovering from Data the Structure of Classical Bayesian Networks

We give some quantum circuits for calculating the probability P(G|D) of a graph G given data D. G together with a transition probability matrix for each node of the graph, constitutes a Classical Bayesian Network, or CB net for short. Bayesian methods for calculating P(G|D) have been given before (the so called structural modular and ordered modular models), but these earlier methods were designed to work on a classical computer. The goal of this paper is to “quantum computerize” those earlier methods.